Collective processes in planetary rings

The aim of this paper is to study numerically the equilibrium properties of planetary rings in a small local quadratic patch with periodic boundary conditions. Contrary to previous approaches, we use a special TREE-code to compute the long-range gravitational interaction between the equal sized particles in our molecular dynamics model. The main result of the simulations is the presence of coherent trailing particle chains at all levels of the optical depth. We find that the height-corrected stability number Q of Toomre in relaxed equilibrium disks cannot fall below a critical value, which lies about Qc ∼ 2.5 for a Keplerian shear flow. Especially in cases of high optical depths the self-excited coherent trailing “wakes” are precursors for small moonlets in the disk. Therefore we believe that the most promising explanation for the fine scale ringlet structure of the B-ring of Saturn is the assumption that a great number of moonlets is orbiting inside the dense particle disk.